Abstract

This paper analyzes various methods that have been developed recently for constructing a classical model for a finite set of quantum mechanical states (electronic states for our applications) and also shows how one of them, the spin matrix mapping method of Meyer and Miller, can be generalized in two aspects. First, it is shown how the methodology can be modified to obtain a classical model of any desired number of degrees of freedom, rather than only one degree of freedom as before. Second, it is shown how the method can be applied in the adiabatic representation, so as to be able to use directly the adiabatic potential energy surfaces and nonadiabatic coupling elements produced by a quantum chemistry calculation.